Can not eating enough food cause vomiting and diahrea? the doctor's don't know what could be wrong.?

we've been to several doctors and not one has been able to expalin why my daughter constantly has an upset stomach. for about 1 week every month, she ends up with the 'stomach flu,' but it's not the flu. She doesn't eat very much, so we are curious to see if having lack of food in her diet could be causing her to be sick. She doesn't have any other symptoms - no fever or body achiness or anything like that. they have checked her organs and they are all fine (no swelling or anything). She doesn't have appendisitis or a gall bladder problem, and they have done blood work and everything has come up normal.